Fractional equations of interrupted subdiffusion

Subdiffusion occurs in systems in which random walk of molecules is very hindered. This process is described by the subdiffusion equation with the Caputo or the Riemann-Liouville fractional time derivative. In some processes molecules can be suddenly eliminated from further subdiffusion. We consider subdiffusion with two elimination processes: when molecules become permanently immobilized or when they disappear due to their decay. The first process is described by the subdiffusion equation with a modified Riemann-Liouville time derivative. The second one is described by both the ordinary subdiffusion equation and the molecule decay equation with the fractional Caputo time derivative with respect to another function. The aim is to compare both models, in particular to derive a formula allowing to assess which of the considered processes is more effective in interrupting subdiffusion of molecules in the long time limit.